Fast Fourier

I gave two talks here is the first:


Fast Fourier Transforms
in less than 15 min!

What is 'Fast Fourier Transforms?

Fast Fourier Transform algorithms are used to compute the Discrete Fourier Transform and its inverse.

Ok, so what is 'Discrete Fourier Transform?

Discrete Fourier Transforms are used to transform one function into another that is called the Frequency domain. This makes sense because in Digital Signal processing we don't care nearly as much about the numbers as we do the FREQUENCY they are observed! Plus, the frequency is usually a less complicated number then the original input.

Still with me? Lets talk more about the Frequency Domain!

We can think of the Fourier Transform as converting the signal information to a magnitude and phase component of each frequency. Now instead of the signal input potentially being all over the place (think eye blinks or other artifacts in EEG data) the current signal in influenced by all of the previous signals and therefore cannot leave the bound of the Frequency Domain!

(Drawing time!)

Oh no, close your eyes, now its time for the math...


So this is a basic Discrete Fourier Transform. The most notable aspect is e^ -(2πi/n), this is like a log curve so every point in the signal with be plotted along this curve.

(More Drawing time!)

That wasn't so bad lets close with a list of advantages and disadvantages:

Advantages:

• Fast! Or at least faster than trying to process the un-transformed signal

Disadvantages:

• Loss of precision due to floating point numbers
• Signal segments are discrete and calculated independently. In this aspect this signal isn't very efficient

The next chapter in this exciting series:
Fast Fourier vs Autoregressive analysis